dr Evaluate the integral: 2² (A) Which trig substitution is correct for this integral? Or=2 sin(0) Or=2 sec (0) Or=2 tan(0) Oz = 4 sin(0) = 4 sec(0) Or = 4 tan(0) (B) Determine the sides of the triangle: (1= A B C II || 0 с A B (C) Which integral do you obtain after substituting for ? Simplify as much as possible. Note: to enter 8, type the word theta. de (D) What is the value of the above integral in terms of ? (Don't forget the + C.) (E) What is the value of the original integral in terms of z? (Don't forget the +C.)
dr Evaluate the integral: 2² (A) Which trig substitution is correct for this integral? Or=2 sin(0) Or=2 sec (0) Or=2 tan(0) Oz = 4 sin(0) = 4 sec(0) Or = 4 tan(0) (B) Determine the sides of the triangle: (1= A B C II || 0 с A B (C) Which integral do you obtain after substituting for ? Simplify as much as possible. Note: to enter 8, type the word theta. de (D) What is the value of the above integral in terms of ? (Don't forget the + C.) (E) What is the value of the original integral in terms of z? (Don't forget the +C.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Evaluate the Integral:**
\[ \int \frac{1}{x \sqrt{4 + x^2}} \, dx \]
**(A) Which trig substitution is correct for this integral?**
- \( x = 2 \sin(\theta) \)
- \( x = 2 \sec(\theta) \)
- \( x = 2 \tan(\theta) \)
- \( x = 4 \sin(\theta) \)
- \( x = 4 \sec(\theta) \)
- \( x = 4 \tan(\theta) \)
**(B) Determine the sides of the triangle:**
*Diagram Description:*
A right triangle is shown with angle \(\theta\) at one of its acute angles. The sides are labeled as follows:
- \( A \) is adjacent to \(\theta\)
- \( B \) is opposite to \(\theta\)
- \( C \) is the hypotenuse
**Side Lengths:**
- \( A = \) [Input Box]
- \( B = \) [Input Box]
- \( C = \) [Input Box]
**(C) Which integral do you obtain after substituting for \( x \)? Simplify as much as possible.**
*Note: to enter \(\theta\), type the word theta.*
\[ \int \] [Input Box] \( \, d\theta \)
**(D) What is the value of the above integral in terms of \(\theta\)? (Don’t forget the \(+C\).)**
[Input Box]
**(E) What is the value of the original integral in terms of \( x \)? (Don’t forget the \(+C\).)**
[Input Box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4effdf1a-67d0-42fb-b95c-7c4b54ad0624%2F07c159b0-4211-497b-b043-1919b11c7b10%2Fyy0a5e_processed.png&w=3840&q=75)
Transcribed Image Text:**Evaluate the Integral:**
\[ \int \frac{1}{x \sqrt{4 + x^2}} \, dx \]
**(A) Which trig substitution is correct for this integral?**
- \( x = 2 \sin(\theta) \)
- \( x = 2 \sec(\theta) \)
- \( x = 2 \tan(\theta) \)
- \( x = 4 \sin(\theta) \)
- \( x = 4 \sec(\theta) \)
- \( x = 4 \tan(\theta) \)
**(B) Determine the sides of the triangle:**
*Diagram Description:*
A right triangle is shown with angle \(\theta\) at one of its acute angles. The sides are labeled as follows:
- \( A \) is adjacent to \(\theta\)
- \( B \) is opposite to \(\theta\)
- \( C \) is the hypotenuse
**Side Lengths:**
- \( A = \) [Input Box]
- \( B = \) [Input Box]
- \( C = \) [Input Box]
**(C) Which integral do you obtain after substituting for \( x \)? Simplify as much as possible.**
*Note: to enter \(\theta\), type the word theta.*
\[ \int \] [Input Box] \( \, d\theta \)
**(D) What is the value of the above integral in terms of \(\theta\)? (Don’t forget the \(+C\).)**
[Input Box]
**(E) What is the value of the original integral in terms of \( x \)? (Don’t forget the \(+C\).)**
[Input Box]
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For answer in part "E", is the answer 1/2 ln| sqrt(x^2+4/x^2) - 2/x |+C or 1/2 ln| sqrt(x^2+4) / x^2 - 2/x| + C? Are we just square rooting (x^2+4) and dividing it by x^2 or are we sqaure rooting the whole ((x^2+4)/x^2)
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